What do the following two equations represent? $-x+3y = 3$ $5x-15y = 2$
Putting the first equation in $y = mx + b$ form gives: $-x+3y = 3$ $3y = x+3$ $y = \dfrac{1}{3}x + 1$ Putting the second equation in $y = mx + b$ form gives: $5x-15y = 2$ $-15y = -5x+2$ $y = \dfrac{1}{3}x - \dfrac{2}{15}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.